Answer:
We conclude that the equation represents the line that passes through the points (4, 5) and (-3, -2) is:
Step-by-step explanation:
Given that the line passes through the points
1 of 3 steps
Determine the slope
Determine the slope of the equation containing the points (4, 5) and (-3, -2) using the formula
[tex]\:m=\frac{y_2-y_1}{x_2-x_1}[/tex]
where m is the slope between (x₁, y₁) and (x₂, y₂)
now substitute (x₁, y₁) = (4, 5) and (x₂, y₂) = (-3, -2)
[tex]\:m=\frac{y_2-y_1}{x_2-x_1}[/tex]
[tex]m=\frac{-2-5}{-3-4}[/tex]
refine
[tex]m=1[/tex]
Thus, the slope of the line is: [tex]m=1[/tex]
Important Tip:
We know that the slope-intercept of the line equation is
[tex]y = mx + b[/tex]
where
- [tex]m[/tex] is the slope
- [tex]b[/tex] is the y-intercept
2 of 3 steps
Determine the y-intercept
now substitute m = 1 and (x, y) = (4, 5) in the slope-intercept form of the line equation
[tex]y = mx + b[/tex]
[tex]5 = 1(4) + b[/tex]
[tex]5 = 4 + b[/tex]
switch sides
[tex]4 + b = 5[/tex]
Subtract 4 from both sides
[tex]4+b-4=5-4[/tex]
Simplify
[tex]b=1[/tex]
Thus, the y-intercept b = 1
3 of 3 steps
Substitute the values
Now, all we need to do is to substitute m = 1 and b = 1 in the slope-intercept form of the line equation
[tex]y = mx + b[/tex]
[tex]y = 1(x) + 1[/tex]
[tex]y = x + 1[/tex]
Conclusion:
Therefore, we conclude that the equation represents the line that passes through the points (4, 5) and (-3, -2) is:
Hence, option a is correct.
Please also check the attached graph.
