Question

"Write the equation of the line passing through (-2,5) and (1,-4) in point-slope form, then rewrite it in slope-intercept form."

Procedure:

Given: Two points (-2,5) and (1,-4).
Determine the slope (m).
Write the equation in point-slope form: y - y1 = m(x - x1).
Rewrite the equation in slope-intercept form: y = mx + b.

Answer 1

Point-Slope Form is y - y1 = -3*(x - x1)

Slope-intercept form is y = -3x - 1

Step-by-step explanation:

Point-slope form of a straight line is y-y₁=m(x-x₁).

(x,y) is (-2,5)

(x₁,y₁) is (1,-4)

y-y₁ = m(x-x₁).

5-(-4) = m(-2-1)

9 = -3m

m = -3

Point-Slope Form is y - y1 = -3*(x - x1)

Slope-Intercept form is y = mx + b

We already know m, the slope, is -3, but lets find it again using a Rise/Run calculation. Rise/Run is the slope. Rise is the change in y and Run is the change in x between the two given points.

Going from (-2,5) to (1,-4):

Rise is -4 - 5 = -9

Run is 1 - (-2) = 3

Rise/Run (m, the slope) becomes -9/3 or -3

We can then write y = -3x + b

We need a value of b that shifhts the line so that it intersects both given points. Find b by entering one of the points into the above equation and solving for b:

y = -3x + b

-4 = -3*1 + b for (1,-4)

b = -1

The equation of the line in slope-intercept form is y = -3x - 1

See the attached graph.

Answer 2

To find the equation of the line passing through (-2,5) and (1,-4) in point-slope form, first find the slope. Then, use the point-slope form to write the equation. Finally, rewrite the equation in slope-intercept form.

Step-by-step explanation:

To find the equation of the line passing through (-2,5) and (1,-4) in point-slope form, we first need to find the slope (m) of the line using the formula m = (y2 - y1) / (x2 - x1). Plugging in the coordinates, we get m = (-4 - 5) / (1 - (-2)) = -9 / 3 = -3.

Next, we can use the point-slope form y - y1 = m(x - x1), where (x1, y1) is one of the given points. Plugging in the slope and one of the points, we have y - 5 = -3(x - (-2)). Simplifying, we get y - 5 = -3x - 6.

To rewrite the equation in slope-intercept form y = mx + b, we need to isolate y. Adding 5 to both sides, we get y = -3x - 1.