write an equation of the line containing the given point and parallel to the given line; use y=mx+b form; (5,8) x+4y=7 i keep getting this wrong. Can someone show me how to work this? Thank you so much

since the new line is parallel to the old line, their slopes must be the same, that is

the new equation must look like this

x+4y = c
plug in the new point (5,8)
5 + 32 = c
c = 37

so the new equation is x + 4y = 37

now change this to the form y = mx + b
4y = - x + 37
y = (-1/4)x + 37/4

To find the equation of a line that is parallel to a given line and passes through a given point, you need to follow these steps:

Step 1: Determine the slope of the given line.
Step 2: Use the slope of the given line and the coordinates of the given point to find the slope-intercept form equation.
Step 3: Rewrite the equation in the slope-intercept form (y = mx + b) to get the final answer.

Let's work through the steps using the given information.

Step 1: Determine the slope of the given line.
The equation of the given line is x + 4y = 7. To determine the slope, we need to rewrite the equation in slope-intercept form (y = mx + b).

x + 4y = 7
4y = -x + 7
y = -(1/4)x + 7/4

The slope of the given line is -1/4.

Step 2: Use the slope of the given line and the coordinates of the given point to find the slope-intercept form equation.
The point given is (5,8), and the slope of the given line is -1/4.

y = mx + b
8 = -(1/4)(5) + b

Simplify the equation:

8 = -(5/4) + b

Step 3: Rewrite the equation in the slope-intercept form (y = mx + b) to get the final answer.
To solve for b, isolate it by adding (5/4) to both sides:

8 + 5/4 = b
(32/4) + (5/4) = b
37/4 = b

Now that we have the value of b, we can write the final equation:

y = -(1/4)x + 37/4

So the equation of the line parallel to x + 4y = 7, passing through the point (5,8), is y = -(1/4)x + 37/4.