Question

What is the equation in slope - intercept form for the line that passes throught the points (-4,1) and (-3,0)

Answer 1

y = − x − 3

Explanation:

• To find the equation of a line in slope-intercept form (y = mx + b) that passes through the points (-4, 1) and (-3, 0), you first need to calculate the slope (m) and then find the y-intercept (b).

• The formula for calculating the slope (m) between two points (x1, y1) and (x2, y2) is:

`\sf m=(y_2-y_1)/(x_2-x_1)`

• Using the points (-4, 1) and (-3, 0):

`\sf m=(0-1)/(-3-(-4)) \\\\m=-1`

• Now that we have the slope (m), we can use one of the given points (let's use (-4, 1)) and substitute it into the slope-intercept equation (y = mx + b) to solve for the y-intercept (b):

1 = ( −1 ) ( −4 ) + b

1 = 4 + b

• Now, solve for b:

b = 1 − 4

b = −3

• So, the equation of the line in slope-intercept form is:

y = − x − 3