Question

Use the graph to find slope and y-intercept of the line. Compare the values to the equation y= -x +4

Answer 1

A line can be written in slope-intercept form, which is

$y=mx+b$

where m represents the slope and b the y-intercept.

The y-intercept is the point where the graph cuts the y-axis. Analyzing the graph we can see the y-intercept is (0, 4), which means that b = 4. Using any other point of this line, we can calculate the slope since we already know the y-intercept.

Let's use the x-intercept, (4, 0). Evaluating this point in our line equation, we have

$\begin{gathered} 0=m\cdot(4)+4 \\ 0=4m+4 \\ 4m=-4 \\ m=-\frac{4}{4} \\ m=-1 \end{gathered}$

Then, our line equation is

$y=-x+4$

Which is equal to the equation given.