{"id":97630,"date":"2021-12-06T15:45:32","date_gmt":"2021-12-06T21:45:32","guid":{"rendered":"https:\/\/www.mometrix.com\/academy\/?page_id=97630"},"modified":"2026-03-28T12:23:32","modified_gmt":"2026-03-28T17:23:32","slug":"key-features-of-linear-function-graphs","status":"publish","type":"page","link":"https:\/\/www.mometrix.com\/academy\/key-features-of-linear-function-graphs\/","title":{"rendered":"Key Features of Linear Function Graphs Overview"},"content":{"rendered":"

There are many ways to graph a linear function. If the linear function is given in slope-intercept form, use the slope and y-intercept that can be identified from the function, \\(y=mx+b\\).<\/p>\n

Linear Function Graph Sample Questions<\/a><\/div>\n

To graph \\(y=\\frac{2}{3}x-4\\), which is written in slope-intercept form<\/a>, we know, the \\(y\\)-intercept, which is where the line intersects the \\(y\\)-axis, is \\(-4\\). We start by plotting a point at \\((0,-4)\\). The slope of the line, which determines the steepness of the line, is \\(\\frac{2}{3}\\).<\/p>\n

The slope<\/a> of a line is also defined as \\(\\frac{\\text{rise}}{\\text{run}}\\), therefore, move up two units and to the right three units to find the next point on the line, which is \\((3,-2)\\). Repeat one more time from \\((3,-2)\\), move up three units and to the right two units to find the point \\((6,0)\\), which happens to be the \\(x\\)-intercept, or the point where the line intersects the \\(x\\)-axis, this is also called the zero<\/strong> of the linear function, which is the value of the independent variable when the value of the dependent variable is zero. Connect the dots to create the graph of the linear function.<\/p>\n

\"graph<\/p>\n

Example:<\/h3>\n

Here is the graph of a linear function.
\n\"graph
\nIdentify the slope, \\(y\\)-intercept, and \\(x\\)-intercept of the linear function.<\/p>\n

<\/div>\n

The \\(y\\)-intercept is the point where the linear function intersects the \\(y\\)-axis, which is (0, 2). The \\(x\\)-intercept is the point where the linear function intersects the \\(x\\)-axis, which is \\((-4,0)\\). The slope is found by dividing the rise by the run between two points. Use the \\(x\\)-intercept, \\((-4,0)\\), as a starting point, how many units do we rise, which is a vertical movement, and run, which is a horizontal movement, to get to the next point, which is \\((-2,1)\\)? In this case, we go up one unit and to the right two units to get to the next point, therefore, the slope of the line is \\(\\frac{1}{2}\\).<\/p>\n\"Click<\/a>\n

Key Features of Linear Function Graphs Sample Questions<\/h2>\n

Here are a few sample questions going over key features of linear function graphs.
\n\n\t\t\t\t

\n\t\t\t\t\tQuestion #1:<\/strong>\n\t\t\t\t\t

 
\nWhat is the \\(y\\)-intercept of the following linear function?<\/p>\n

\\(y=-2x+8\\)<\/div>\n<\/div>\n\t\t\t\t\t
\\((-2,0)\\)<\/div>
\\((0,-2)\\)<\/div>
\\((0,8)\\)<\/div>
\\((8,0)\\)<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t\t