Question

Write the equation in slope intercept form: passing through the x-axis at x=3 and passing through the y-axis at y= -5

Answer 1

Answer:

$y=\frac{5}{3}x-5$

Step-by-step explanation:

Slope-intercept:

$y=mx+b$

m is the slope and b is the y-intercept. We know that the line passes through the y-axis at -5, so this is the y-intercept (where x is equal to 0). Insert this into the equation:

$y=mx-5$

With the given information, we can form two points:

$(3,0)(0,-5)$

The first one is the x-intercept and the second the y-intercept. Use these to find the slope:

$\frac{y_{2}-y_{1}}{x_{2}-x_{1}}=\frac{rise}{run}$

Rise over run is the change in the y-axis over the change in the x-axis, otherwise known as the slope. Insert the appropriate values:

$(3_{x1},0_{y1})\\(0_{x2},-5_{y2})\\\\\frac{-5-0}{0-3}$

Solve:

$\frac{-5-0}{0-3}=\frac{-5}{-3}$

Note that both the numerator and denominator are negatives. Two negatives make a positive, so:

$\frac{5}{3}$

The slope is $\frac{5}{3}$

Insert into the equation:

$y=\frac{5}{3}x-5$

:Done