1. Write the equation of the line that passes through the given point and has the given slope. Write the answer in slope-intercept form. Through: (5,2), slope = 6/5
2. Write the equation of the line that passes through the given point and has the given slope. Write the answer on slope-intercept form. Through: (5,-2), slope = -1/5
3. Write the equation of the line that passes through the given two points. Write the answer in slope-intercept form. Through: (-3,7) and (1,-1)
1. The equation of the line is y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope is 6/5 and the point is (5,2), we can use the point-slope form to find b.
Using the equation (y - y1) = m(x - x1), we have (y - 2) = (6/5)(x - 5).
Simplifying, we get y - 2 = (6/5)x - 6.
Rearranging, the equation becomes y = (6/5)x - 4.
2. Using a similar approach, the equation of the line passing through (5,-2) with a slope of -1/5 is given by:
(y - (-2)) = (-1/5)(x - 5).
Simplifying, we have y + 2 = (-1/5)x + 1.
Rearranging, the equation becomes y = (-1/5)x - 1.
3. To find the equation of the line passing through (-3,7) and (1,-1), we can use the slope-intercept form.
First, we find the slope using the formula: m = (y2 - y1)/(x2 - x1).
Substituting the coordinates, we have m = (-1 - 7)/(1 - (-3)) = -8/4 = -2.
The equation of the line is then y = mx + b.
Using a point from one of the given points (let's use (-3,7)), we substitute the values to find b.
We have 7 = -2(-3) + b, which simplifies to 7 = 6 + b.
Solving for b, we get b = 7 - 6 = 1.
Therefore, the equation of the line is y = -2x + 1.