[latex]y[\/latex]-intercept of a Line<\/h3>\r\nThe [latex]y[\/latex]-intercept of a function is the value of [latex]f(x)[\/latex] when [latex]x = 0[\/latex].\r\nIn slope-intercept form, [latex]f(x) = mx + b[\/latex], the [latex]y[\/latex]-intercept is the constant [latex]b[\/latex].\r\n\r\n \r\n\r\nIn context, the [latex]y[\/latex] typically represents the initial value or starting point of the function.\r\n\r\n<\/section>\r\nFind the [latex]y[\/latex]-intercept of the following:<\/h3>\r\n
[latex]f\\left(x\\right)=\\frac{1}{2}x - 3[\/latex]<\/p>\r\n
[reveal-answer q=\"400057\"]Show Solution[\/reveal-answer]
[hidden-answer a=\"400057\"]
Substitute [latex]x = 0[\/latex] into the function:<\/p>\r\n
[latex]\\begin{array}{l}f(0)=\\frac{1}{2}(0) - 3\\ f(0)=0 - 3\\ f(0)=-3\\end{array}[\/latex]<\/p>\r\n
The graph crosses the [latex]y[\/latex]-axis at the point [latex](0, -3)[\/latex].
[latex]\\[\/latex]
Analysis of the Solution<\/strong>
A graph of the function is shown below. We can see that the line crosses the [latex]y[\/latex]-axis at [latex]-3[\/latex], confirming the [latex]y[\/latex]-intercept.\r\n[\/hidden-answer]<\/p>\r\n\r\n<\/section>Find the [latex]y[\/latex]-intercept of the graph. ![](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/1227\/2015\/04\/03010639\/CNX_Precalc_Figure_02_01_0132.jpg\")
\r\n[reveal-answer q=\"400058\"]Show Solution[\/reveal-answer]
[hidden-answer a=\"400058\"]
The [latex]y[\/latex]-intercept is the point where the line crosses the [latex]y[\/latex]-axis. On this graph, the [latex]y[\/latex]-intercept is [latex](0,-7)[\/latex].\r\n[\/hidden-answer]<\/p>\r\n\r\n<\/section>The [latex]y[\/latex]-intercept is always written in the form [latex](0,y)[\/latex].<\/section>[ohm_question hide_question_numbers=1]317629[\/ohm_question]<\/section><\/section>","rendered":"Finding the [latex]y[\/latex]-intercept of a Line<\/h2>\n
Another key feature of a linear function is the [latex]y[\/latex]-intercept: the point at which the graph of a function crosses the [latex]y[\/latex]-axis. The [latex]y[\/latex]-intercept is the [latex]y[\/latex]-coordinate of the point where the input value is zero.<\/p>\n
To find the [latex]y[\/latex]-intercept, substitute [latex]x = 0[\/latex] into the function and solve for [latex]f(x)[\/latex] or [latex]y[\/latex]. For example, consider the function shown:<\/p>\n
[latex]f\\left(x\\right)=3x - 6[\/latex]<\/p>\n
Substitute [latex]x = 0[\/latex] into the function:<\/p>\n
[latex]\\begin{array}{l}f(0)=3(0) - 6\\hfill \\\\ f(0)=0 - 6\\hfill \\\\ f(0)=-6\\hfill \\end{array}[\/latex]<\/p>\n
The graph of the function crosses the [latex]y[\/latex]-axis at the point [latex](0, -6)[\/latex].<\/p>\n\n[latex]y[\/latex]-intercept of a Line<\/h3>\n
The [latex]y[\/latex]-intercept of a function is the value of [latex]f(x)[\/latex] when [latex]x = 0[\/latex].
\nIn slope-intercept form, [latex]f(x) = mx + b[\/latex], the [latex]y[\/latex]-intercept is the constant [latex]b[\/latex].<\/p>\n
<\/p>\n
In context, the [latex]y[\/latex] typically represents the initial value or starting point of the function.<\/p>\n<\/section>\n\nFind the [latex]y[\/latex]-intercept of the following:<\/h3>\n
[latex]f\\left(x\\right)=\\frac{1}{2}x - 3[\/latex]<\/p>\n
\n
Find the [latex]y[\/latex]-intercept of the following:<\/h3>\r\n
[latex]f\\left(x\\right)=\\frac{1}{2}x - 3[\/latex]<\/p>\r\n
[reveal-answer q=\"400057\"]Show Solution[\/reveal-answer]
[hidden-answer a=\"400057\"]
Substitute [latex]x = 0[\/latex] into the function:<\/p>\r\n
[latex]\\begin{array}{l}f(0)=\\frac{1}{2}(0) - 3\\ f(0)=0 - 3\\ f(0)=-3\\end{array}[\/latex]<\/p>\r\n
The graph crosses the [latex]y[\/latex]-axis at the point [latex](0, -3)[\/latex]. [reveal-answer q=\"400058\"]Show Solution[\/reveal-answer] Another key feature of a linear function is the [latex]y[\/latex]-intercept: the point at which the graph of a function crosses the [latex]y[\/latex]-axis. The [latex]y[\/latex]-intercept is the [latex]y[\/latex]-coordinate of the point where the input value is zero.<\/p>\n To find the [latex]y[\/latex]-intercept, substitute [latex]x = 0[\/latex] into the function and solve for [latex]f(x)[\/latex] or [latex]y[\/latex]. For example, consider the function shown:<\/p>\n [latex]f\\left(x\\right)=3x - 6[\/latex]<\/p>\n Substitute [latex]x = 0[\/latex] into the function:<\/p>\n [latex]\\begin{array}{l}f(0)=3(0) - 6\\hfill \\\\ f(0)=0 - 6\\hfill \\\\ f(0)=-6\\hfill \\end{array}[\/latex]<\/p>\n The graph of the function crosses the [latex]y[\/latex]-axis at the point [latex](0, -6)[\/latex].<\/p>\n The [latex]y[\/latex]-intercept of a function is the value of [latex]f(x)[\/latex] when [latex]x = 0[\/latex]. <\/p>\n In context, the [latex]y[\/latex] typically represents the initial value or starting point of the function.<\/p>\n<\/section>\n [latex]f\\left(x\\right)=\\frac{1}{2}x - 3[\/latex]<\/p>\n \n
[latex]\\[\/latex]
Analysis of the Solution<\/strong>
A graph of the function is shown below. We can see that the line crosses the [latex]y[\/latex]-axis at [latex]-3[\/latex], confirming the [latex]y[\/latex]-intercept.\r\n[\/hidden-answer]<\/p>\r\n\r\n<\/section>\r\n
[hidden-answer a=\"400058\"]
The [latex]y[\/latex]-intercept is the point where the line crosses the [latex]y[\/latex]-axis. On this graph, the [latex]y[\/latex]-intercept is [latex](0,-7)[\/latex].\r\n[\/hidden-answer]<\/p>\r\n\r\n<\/section>Finding the [latex]y[\/latex]-intercept of a Line<\/h2>\n
[latex]y[\/latex]-intercept of a Line<\/h3>\n
\nIn slope-intercept form, [latex]f(x) = mx + b[\/latex], the [latex]y[\/latex]-intercept is the constant [latex]b[\/latex].<\/p>\nFind the [latex]y[\/latex]-intercept of the following:<\/h3>\n