slope intercept form for (-3,2),(1,3)
To find the slope-intercept form of a linear equation, we need to determine the slope (m) and the y-intercept (b).
Given the points (-3,2) and (1,3), we can find the slope (m) using the formula:
m = (y₂ - y₁) / (x₂ - x₁)
By substituting the coordinates into the formula, we get:
m = (3 - 2) / (1 - (-3))
m = 1 / 4
Now that we have the slope (m), we can use one of the points, let's say (-3,2), and the slope in the point-slope form of a linear equation:
y - y₁ = m(x - x₁)
By substituting the value of m and the coordinates of the point into the equation, we get:
y - 2 = (1/4)(x - (-3))
y - 2 = (1/4)(x + 3)
Next, we can distribute the (1/4) to simplify the equation:
y - 2 = (1/4)x + (1/4)(3)
y - 2 = (1/4)x + 3/4
Finally, we can rearrange the equation to the slope-intercept form (y = mx + b), where b represents the y-intercept:
y = (1/4)x + 3/4 + 2
y = (1/4)x + 3/4 + 8/4
y = (1/4)x + 11/4
Therefore, the slope-intercept form of the linear equation passing through the points (-3,2) and (1,3) is y = (1/4)x + 11/4.