Write the equation of the line in slope intercept form:
(4, 7); m = -3/8
y = -(3/8)x + b
7 = -(3/8)4 + b
7 = -3/2 + b
14/2 = -3/2 + b
b = 17/2
so
y = -(3/8)x + 17/2
The slope-intercept form of a line is y = mx + b, where m is the slope and b is the y-intercept.
Given that the slope (m) is -3/8, and the point (4, 7) lies on the line, we can substitute these values into the equation.
y = mx + b
7 = (-3/8)(4) + b
To find the value of b, we can solve for it:
7 = (-3/8)(4) + b
7 = -3/2 + b
7 + 3/2 = b
14/2 + 3/2 = b
17/2 = b
Therefore, the equation of the line in slope-intercept form is y = (-3/8)x + 17/2.
To write the equation of the line in slope-intercept form, which is in the form of y = mx + b, where m represents the slope and b represents the y-intercept, follow these steps:
Step 1: Start with the given slope and the coordinates of a point on the line. In this case, the given slope is m = -3/8, and the coordinates of a point on the line are (4, 7).
Step 2: Plug in the values of the slope (m), the x-coordinate (x), and the y-coordinate (y) into the equation y = mx + b. Using the given point (4, 7), it becomes:
7 = (-3/8)(4) + b
Step 3: Simplify the equation by multiplying -3/8 and 4:
7 = -3/2 + b
Step 4: Isolate the variable b by adding 3/2 to both sides:
7 + 3/2 = b
Step 5: Combine the numerical terms on the left side:
17/2 = b
Step 6: Rewrite the equation using the value of b and the derived slope:
The equation of the line in slope-intercept form is y = -3/8x + 17/2.
Therefore, the equation of the line in slope-intercept form for the given slope m = -3/8 and point (4, 7) is y = -3/8x + 17/2.