Find an equation for a line given the slope and a point

by Stephanie
(Canada)

Question
Find an equation for a line with a slope of 2/3 and passing through (1, –4).

Answer
STEP 1:   We are given the slope and a point through which the line passes. With these values, and the slope-intercept form, the equation of the line can be determined. By the slope-intercept form, we refer to an equation of the form:
                                        y = mx + b

Make a note of what each variable in the equation stands for:

slope and y intercept

Use 2/3 for m in the equation.

substituting 2/3 into m

STEP 2:    The value of b is still unknown. Since the line is said to pass through (1, –4), we can substitute the respective values for x and y.

substituting point (1,-4) into the equation

STEP 3: Now, solve the equation for b.

calculating for b

STEP 4: The final step is to replace all the variables in the slope-intercept form with the known values.

the final equation of a line

The equation of the line is:

slope and y intercept

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