Question

Which equation describes the line that passes through (-4,3) and (4.5)?

a)y=4x + 2 / 2
b)y = 15 +4
c)y = 4x
d)y = 4x + 4

Answer 1

The equation that describes the line passing through (-4,3) and (4,5) is y = 4x + 4.

Step-by-step explanation:

The equation that describes the line passing through (-4,3) and (4,5) is y = 4x + 4. To find the equation of a line given two points, we first calculate the slope using the formula: m = (y2 - y1) / (x2 - x1). Using the coordinates (-4,3) and (4,5), we get m = (5 - 3) / (4 - (-4)) = 2/8 = 1/4. The slope-intercept form of the equation is y = mx + b, where m is the slope and b is the y-intercept. Plugging in the values of m and one of the points (4,5), we can solve for b: 5 = (1/4)(4) + b. Solving for b, we find b = 4. Therefore, the equation of the line is y = 4x + 4.

Answer 2

The equation that describes the line passing through (-4,3) and (4,5) is y = 0.5x + 4.

Step-by-step explanation:

To determine the equation of a line given two points, we employ the slope-intercept form y = mx + b, where m represents the slope and b denotes the y-intercept.

Begin by calculating the slope (m) using the formula:

m = (y₂ - y₁) / (x₂ - x₁)

For the points (-4,3) and (4,5), substitute the values:

m = (5 - 3) / (4 - (-4)) = 2 / 8 = 1 / 4

Now, with the slope identified, select one of the points (let's use (-4,3)) and substitute the values into the slope-intercept form to determine the y-intercept (b):

3 = (1 / 4)(-4) + b

Solving for b:

3 = -1 + b

b = 4

Thus, the equation of the line is y = 0.5x + 4. To simplify, multiply both sides by 2:

2y = 0.5x + 8

y = 0.5x + 4

Consequently, the equation describing the line passing through (-4,3) and (4,5) is y = 0.5x + 4.