Write the slope-intercept equation for the line that passes through(4,3) and has slope 5/4
To write the slope-intercept equation for a line, we use the formula:
y = mx + b
Where:
- y represents the y-coordinate of a point on the line
- x represents the x-coordinate of the same point on the line
- m represents the slope of the line
- b represents the y-intercept of the line
Given that the line passes through the point (4,3) and has a slope of 5/4, we can substitute these values into the equation to find the y-intercept (b).
Let's start by substituting the values we know into the equation:
3 = (5/4)(4) + b
To simplify, multiply the slope (5/4) by 4:
3 = (5/4)(4) + b
3 = 5 + b
Now, isolate b by subtracting 5 from both sides of the equation:
3 - 5 = b
-2 = b
We have found that the y-intercept (b) is -2.
So, the slope-intercept equation for the line is:
y = (5/4)x - 2