Use distributive property <em>a(b + c) = ab + ac</em>
4(x + 2) - 3(7 + y) = (4)(x) + (4)(2) + (-3)(7) + (-3)(y)
= 4x + 8 - 21 - 3y = 4x - 3y - 13
You are looking for the slope and y intercept to complete the equation of the line.
The equation of a line is in something called slope intercept form. That looks like y = mx + b. m represents the slope (measure of how steep a line is, and in which direction it is going) and b represents the y intercept (y coordinate when x = 0). You need to find the slope and y intercept to complete the equation.
First, find the slope. The formula for slope is: m = (y2 - y1)/(x2 - x1) where m is the slope and (x1, y1) and (x2, y2) are points.
Pick any two points on the graph. I will use (-2, 0) and (0, 4). Now use these values to find the slope.
m = (4-0)/(0+2) = 4/2
m = 2
m = 2 means that for every two units the line goes up on the y axis, it moves one to the right on the x axis. 2 will go in your first box.
Now find the y intercept. The y intercept is where the line crosses the y axis - it is the y coordinate when x = 0. Here when x = 0, y = 4, so your y intercept is at 4. 4 goes into your second box.
The equation is y = 2x + 4
y-intercept: Let x = 0 and solve for y:
(x-1)^2 + (y-2)^2 = 10 => (-1)^2 + y^2 - 4y + 4) = 10
=> 1 + y^2 - 4y + 4 = 10, or y^2 - 4y -5 = 0
The solutions of this quadratic are y = 5 and y = -1.
Thus, the y-intercepts are (0, 5) and (0, -1).
Now find the x-intercepts: Let y = 0 and solve the resulting equation for x:
(x-1)^2 = 10 - (-2)^2, or (x-1)^2 = 10 - 4 = 6.
Taking the sqrt of both sides, x - 1 = plus or minus sqrt(6), or:
x = 1 +√6 and x = 1 - √6, so that the x-intercepts
are (1+√6, 0) and (1-√6, 0).
Infinite amount of solutions
See attached image
Comment for more help or if the image is too hard to see
Hope this helps :)
Answer:
y=1/4x + 16
Step-by-step explanation:
