Question

Plot the two points on the graph:(0,-4) and (-8,2)graph the line that goes through the two pointsFind the slope by drawing a slope triangle between the two points. Make sure it's simplifiedWrite the equation of the line in slope-intercept form

Answer 1

We are given the following two points

`(0,-4)\: \text{and}\: (-8,2)`

Let us plot these two points on the graph and draw a line through them.

Now let us find the slope by drawing a slope triangle between the two points.

As you can see, the rise (-6) is the vertical distance between the two points on the line.

The run (8) is the horizontal distance between the two points on the line.

So, the slope of the line is

`slope=m=\frac{\text{rise}}{\text{run}}=(-6)/(8)=-(3)/(4)`

Write the equation of the line in slope-intercept form​.

The slope-intercept form is given by

`y=mx+b_{}`

Where m is the slope and b is the y-intercept of the line.

The y-intercept is the point where the line crosses the y-axis.

From the above graph, we see that the line crosses the y-axis at -4

So, the y-intercept is -4

Therefore, the equation of the line in slope-intercept form is

`\begin{gathered} y=mx+b \\ y=-(3)/(4)x-4 \end{gathered}`