Respuesta :
Answer:
y = 7x + 30
Step-by-step explanation:
Lines in algebra are plotted on coordinate planes and are known for their unique characteristics.
One of these is their slope, "a number that describes both the direction and the steepness of a line," which is denoted by m.
The slope of a line is found by dividing the change in vertical distance (y) by the change in horizontal distance (x) between two points on said line.
This is the formula for the slope of a line:
[tex]m = \frac{y_{2}-y_{1} }{x_{2}-x_{1}} \\[/tex]
where m is the slope of the line;
where x1 and y1 describe a specific point (x1, y1) on the line;
where x2 and y2 describe a specific point (x2, y2) on the line;
Another one of these is the y-intercept, "a point where the graph of a function or relation intersects the y-axis of the coordinate system," which is denoted by b.
The y-intercept of a line is found by examining the line graphically. Where a line and the y-axis (the vertical component of the coordinate plane) intersect is considered (0, b) and is the y-intercept.
Now we know how to find the slope and the y-intercept. But what about the actual equation of a line? Lines can be expressed in equations, and they have three forms: slope-intercept, standard, and point-slope.
Equations of lines are usually found in slope-intercept form. This formula helps show the slope and y-intercept of a line directly. The formula is as follows:
y = mx + b
where x and y describe any point (x, y) on the line;
m is the slope of a line;
b describe the y-intercept (0, b) of the line.
Another form of the equation of a line is the standard form. Standard form helps show the x- and y-intecepts of a line directly. It is also useful for matrix operations. This formula is as follows:
Ax + By = C
where x and y describe any point (x, y) on the line;
A, B, and C are constants, preferably integers.
To find the equation of a line given a point and a slope, the point-slope form formula has to be used:
y - y1 = m(x - x1)
where x and y describe any point (x, y) on the line;
where x1 and y1 describe a specific point (x1, y1) on the line;
m is the slope of a line.
FINALLY, we can find out what the equation of this line is.
First, we will assign the point (-6, -12) with variables. Since -6 is our first x-coordinate given and -12 is our first y-coordinate given, we can say that x1 = -6 and y1 = -12.
Then, since we have a slope and a point of a line, we can use point-slope form.
y - y1 = m(x - x1)
m = 7, x1 = -6, and y1 = -12. We substitute these values into the form and simplify.
y - (-12) = 7(x - (-6))
y + 12 = 7(x + 6)
y + 12 = 7x + 42
Then, we rearrange the equation to fit slope-intercept form.
y = 7x + 30
