Find the equation of the line with slope −5 and that contains the point (−9,−5). Write the equation in the form y=mx+b and identify m and b. Find the equation of the line that contains the points (2,4) and (10,2). Write the equation in the form y=mx+b and identify m and b.

Answer & Step-by-step explanation:

Slope-intercept form:

m is the slope and b is the y-intercept. Insert the given slope:

To find the y-intercept, take the given coordinate point and insert:

Solve for b:

Simplify multiplication:

Subtract 45 from both sides:

The y-intercept is -50. Insert:

Use the slope formula for when you have two points:

The slope is the change in the y-axis over the change in the x-axis, or rise over run. Insert the points:

The slope is . Insert:

Now follow the steps from the last problem to find the y-intercept. Choose a point and insert into the equation:

Solve for b:

Simplify multiplication:

Re-insert:

Subtract b from both sides:

Subtract 4 from both sides:

Simplify subtraction:

Re-insert:

Divide both sides by -1 to make the variable positive (can be seen as -1b):

The y-intercept is .

Write the equation:

:Done