Graph the following equation: clculte the slope, x-intercept, and y-intercept, and label the the intercelts on the graph.
problem: Find an equationin slope-intercept form passing through the points (2,5) and ( 7,-3).
(2+5)/(7+ -3) = 7/4
so y = (7/4)x +b
using (-2,5)
5= (7/4)(-2) +b
20= -3.5 +4b
b=?
I just can't see to figure it out
Equation passing through the points (2,5) and ( 7,-3)
Slope m = (-3 - 5)/(7 - 2)
m = -8/5
y = mx + b
y = -8/5 x + b
Using point, (2, 5) to find b
y = -8/5 x + b
5 = -8/5(2) + b
5 = -16/5 + b
b = 5 + 16/5
b = 25/5 + 16/5
b = 41/5
y = -8/5 x + 41/5
In the form, y = mx + b
b = y-intercept
y-intercept = 41/5
An x-intercept is a point on the graph where y is zero.
y = -8/5 x + 41/5
0 = -8/5 x + 41/5
-8/5 x = -41/5
x = -41/5 * -5/8
x = 41/8
x-intercept = 41/8
To find the equation in slope-intercept form passing through the points (2,5) and (7,-3), we need to first find the slope (m) and then use one of the points to substitute into the equation to solve for the y-intercept (b).
Step 1: Calculate the slope (m)
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)
Using the points (2,5) and (7,-3), we can substitute the values into the formula:
m = (-3 - 5) / (7 - 2) = (-8) / 5 = -8/5
Step 2: Substitute one of the points to solve for the y-intercept (b)
We can choose either of the points (2,5) or (7,-3) to substitute into the equation. Let's use the point (2,5).
Substituting the values into the slope-intercept form equation (y = mx + b):
5 = (-8/5)(2) + b
5 = -16/5 + b
To solve for b, we need to isolate it on one side of the equation. Let's add 16/5 to both sides:
5 + 16/5 = -16/5 + b + 16/5
25/5 + 16/5 = b
41/5 = b
Step 3: Write the equation in slope-intercept form
Now that we have the values for the slope (m = -8/5) and the y-intercept (b = 41/5), we can write the equation in slope-intercept form:
y = (-8/5)x + 41/5
To graph the equation, plot both the x-intercept and the y-intercept on the graph. The x-intercept is where the line crosses the x-axis, so when y = 0. In this case, the x-intercept is when y = 0, so we can substitute that into the equation:
0 = (-8/5)x + 41/5
(-8/5)x = -41/5
x = (-41/5) / (-8/5) = 41/8 ≈ 5.125
So the x-intercept is (5.125, 0).
Plot the x-intercept (5.125, 0) and y-intercept (0, 8.2) on the graph, and draw a straight line passing through these two points. This line represents the equation y = (-8/5)x + 41/5.