Answer:
2x+y=7
Step-by-step explanation:
Hi there!
We are given that a line has a y intercept of 7 and passes through the point (1,5)
We want to write the equation of this line in standard form, which is ax+by=c, where a, b, and c are free integer coefficients, but a and b cannot equal zero, and a cannot be negative
To start, we can write the equation of the line in slope-intercept form, which is y=mx+b, where m is the slope and b is the y intercept
We are given that the y intercept is 7, so we can plug it in as b into the equation.
Here is the equation of the line so far:
y=mx+7
Now we need to find m
as the equation passes through the point (1,5) we can use it to help solve for b.
Substitute 1 as x and 5 as y into the equation.
5=m*1+7
Multiply
5=m+7
Subtract 7 form both sides
-2=m
Substitute -2 as m into the equation
y=-2x+7
This is the equation in slope-intercept form
However, remember that we aren't done, as the problem wants us to have the equation in standard form
In standard form, the terms containing x and y are on the same side; right now, they are on opposite sides.
So we can add -2x to both sides in order to move it to the left side
y=-2x+7
+2x +2x
______
2x + y = 7
This is the equation of the line in standard form.
Hope this helps!
If you would like a similar problem for practice, take a look here: https://brainly.com/question/8829271
