Find an equation of the line that satisfies the given conditions.
Through (5, 3) and (4, 7)
The equation of a line is made up of 4 parts: the y intercept, the slope, y,and x. To find the slope, follow the formula y2-y1/x2-x1. 7-3/4-5 = 4/-1 = -4. Choose either of the ordered pairs to be your x and y. Now you have 3 = -4(5) + b. Solve for b by performing the opposite operation (in this case, add 20 to both to isolate b) and you get b = 23. Put it all together and you get:
y = -4x + 23
To find the equation of a line, we can use the slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
First, let's find the slope using the formula: m = (y2 - y1) / (x2 - x1)
Given points: (5, 3) and (4, 7)
x1 = 5, y1 = 3
x2 = 4, y2 = 7
m = (7 - 3) / (4 - 5)
m = 4 / -1
m = -4
Now that we have the slope, we can substitute it into the slope-intercept form along with one of the given points to find the y-intercept.
Using the point (5, 3):
3 = (-4)(5) + b
3 = -20 + b
b = 23
The y-intercept is 23, so the equation of the line is:
y = -4x + 23
To find the equation of a line given two points, we can use the slope-intercept form of the equation, which is y = mx + b.
First, we need to find the slope (m) of the line. The slope of a line passing through two points (x1, y1) and (x2, y2) can be calculated using the formula:
m = (y2 - y1) / (x2 - x1)
Substituting the given points (5, 3) and (4, 7) into the formula, we have:
m = (7 - 3) / (4 - 5)
= 4 / -1
= -4
So, the slope of the line is -4.
Next, we need to find the y-intercept (b) of the line. We can use the point-slope form of the equation, which is y - y1 = m(x - x1), using one of the given points.
Let's use the point (5, 3):
y - 3 = -4(x - 5)
y - 3 = -4x + 20
y = -4x + 23
Therefore, the equation of the line passing through the points (5, 3) and (4, 7) is y = -4x + 23.
First find the slope of the line through those coordinates.
Slope formula:
m = (y2-y1)/(x2-x1)
m=(7-3)/(4-5)
m=4/-1
m=-4
So the slope is -4
Now use the point slope formula:
y-y1=m(x-x1)
y-3 = -4(x-5)
y-3=-4x+20
y=-4x+23
You will get the same result if you use the other coordinates in the point slope formula as well:
y-7=-4(x-4)
y-7=-4x+16
y=-4x+ 23