A line passes through (-3, -2) and is perpendicular to 3x - 2y = 7. What is the equation of the line in slope-intercept form?
Mathematics · High School · Wed Jan 13 2021
Answered on
Given the points:
(-3, -2)
x1= -3
y1 = -2
Write the equation in slope-intercept form.
To do so we must first write in point-slope form.
Point-slope form:
y - y1 =m(x -x1)
Slope-intercept form:
y = mx + b
Solution:
Before we can write in point-slope form, we must first find the slope of the line, we can find the slope by using the slope formula.
m = y1 /x1
m= -2/-3
m = ⅔
Substitute the given values of x1, m and y1 to the formula for the point-slope form.
y - (-2) = ⅔ ( x - (-3))
y + 2 = ⅔ ( x + 3 )
To equate in slope-intercept form, we distribute ⅔ to each value inside the parenthesis, and the transpose 2 to the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.
y + 2 = ⅔x + 2
y = ⅔x + 2 - 2
y = ⅔x
Final answer:
y = ⅔x