find an equation of the line satisfying the conditions. write equation in slope intercept form

Question

through (-6,5), parallel to -7x+5y=57

Answer 1

Write an equation of a line in slope-intercept form that passes through (-6,5), and is parallel to -7x + 5y = 57.

Parallel lines have the the same exact slopes! Thus, let’s rewrite the standard-form of the equation in slope-intercept form (y = my + b) where the slope (m) is more visible.

-7x + 5y = 57 First let’s move -7x to the right side of the

+7x +7x equation. Adding 7x to both sides gives:

5y = 7x + 57 Solve for y by dividing both sides by 5:

y = (7/5)x + (57/5) The slope m is (7/5)

Now using our slope of seven-fifths (7/5), substitute into point-slope form given the point (-6,5)

point-slope form of an equation: y - y1 = m(x - x1)

so, y - 5 = (7/5)(x - (-6)) Simplifying gives:

y - 5 = (7/5)x + (42/5) Finally add 5 to both sides to get

+5 +5 back to slope-intercept form,

y = 7 x + 67 thus solving for y to get:

5

or y = 7 x + 67

5 5

*fraction part: 42 + 5 equals 42 + 25 Equals 67

5 5 5 5

Answer 2

Good afternoon Lexi,

The best approach to this problem is to first write the given equation in the standard format of a line, so we will manipulate the given equation of -7x + 5y = 57 into y = mx + b form:

-7x + 5y = 57

-7x + 5y + 7x = 57 + 7x

5y = 57 + 7x

y = (57+7x)/5

y = 7/5*x + 57/5

We can now clearly see that the slope of the given equation is m = 7/5, and the y intercept b = 57/5.

For lines to be parallel they must share the same slope value, so a line satisfying the condition of being parallel to the given equation will also share a value of m = 7/5. The only remaining condition to satisfy is having this new line cross through the point (-6,5). We have all the necessary information to determine the equation of this new line, the last piece of the puzzle is determining the value for "b" but since we know the X and Y values (-6 and 5 respectively) along with the slope m = 7/5, we can solve for the y-intercept b:

y = 7/5*x + b

5 = 7/5 * -6 + b

5 = -8.4 + b

13.4 = b

This gives us the equation of:

y = 7/5*x + 13.4