Instructions: Use point - slope form of each equation to identify a point the line passes through and slope of the line.
Problem: y-2=3/4(x+9)
y-2=3/4(x+9)
y-2=3/4x+6.75
y=3/4x+8.75
Line L has equation of 4x + 3y = 7. Find equation of the line that is perpendicular to L which passes through the point of intersection of L and the y-axis. Give answer in the form ax + by +c = 0.
To identify a point the line passes through and the slope of the line using the point-slope form of the equation, y - y1 = m(x - x1), we need to rewrite the given equation in the point-slope form.
Given equation: y - 2 = (3/4)(x + 9)
Step 1: Distribute the (3/4) to the terms inside the parentheses.
y - 2 = (3/4)x + (3/4)(9)
Simplifying further, we have:
y - 2 = (3/4)x + 27/4
Step 2: Rearrange the equation to match the point-slope form, y - y1 = m(x - x1), where (x1, y1) represents a point on the line, and m represents the slope of the line.
Let's rewrite the equation:
y = (3/4)x + 27/4 + 2
Simplifying further:
y = (3/4)x + 27/4 + 8/4
y = (3/4)x + 35/4
Now, we have successfully rewritten the equation in slope-intercept form (y = mx + b), where m is the slope of the line and b is the y-intercept.
The slope of the given equation is 3/4.
To find a point on the line, we can just read it from the equation. In this case, the line passes through the point (-9, 35/4).
So, the point the line passes through is (-9, 35/4), and the slope of the line is 3/4.