How would you solve these types of problems? They confuse me!
1. Write the quation of the line that passes through points (-8,-6) and (5,3)
2. Write the equation of the line that passes through (3,-4) and has a slope of 2.
I know that you have to do something with y=mx+b, but I don't know what. I also have a graphing calcluator if that helps with anything.
1. The slope of the line will be
m = (y2-y1)/(x2-x1) = 9/13
The equation will have the form
y-y1 = m(x-x1)
Use x1, y1, and rewrite this as:
y+6 = (9/13)(x+8)
y = (9/13)x -6/13
The same approach will work for #2
how did you get from
y+6 = (9/13)(x+8)
to
y = (9/13)x -6/13 ?
To solve these types of problems, you can use the formula for the equation of a line, which is commonly written as y = mx + b. In this equation, "m" represents the slope, and "b" represents the y-intercept.
Let's break down the steps for each problem:
1. To find the equation of a line that passes through two given points, (-8, -6) and (5, 3), you first need to find the slope of the line. The slope (m) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Plug in the coordinates of the points to find the slope:
m = (3 - (-6)) / (5 - (-8))
Simplify the equation:
m = 9 / 13
Once you have the slope, you can choose one of the given points (let's use (-8, -6)) and substitute the slope into the point-slope form of the equation:
y - y1 = m(x - x1)
Substitute the values:
y - (-6) = (9 / 13)(x - (-8))
Simplify the equation:
y + 6 = (9 / 13)(x + 8)
Lastly, you can rewrite the equation in the slope-intercept form (y = mx + b):
y = (9 / 13)x + (72 / 13) – 6
y = (9 / 13)x + (72 / 13) – (78 / 13)
y = (9 / 13)x – (6 / 13)
2. To find the equation of a line that passes through the point (3, -4) and has a slope of 2, the process is similar.
We can use the point-slope form:
y - y1 = m(x - x1)
Plug in the coordinates and the slope:
y - (-4) = 2(x - 3)
Simplify the equation:
y + 4 = 2x - 6
Rearrange the equation to the slope-intercept form:
y = 2x - 6 - 4
y = 2x - 10
Therefore, the equation of the line is y = 2x - 10.
If you have a graphing calculator, you can also input the coordinates or the slope to find the equation of a line. The process may vary depending on the calculator model, but you can usually find guides or tutorials online that provide specific instructions for your calculator.