Write the equation of the line in slope intercept form; passing through (3,11) with slope 7/3
You know that the equation in the form
y = mx + b
has to be y = (7/3)x + b
plug in the given point:
11 = (7/3)(3) + b
11 = 7 + b
b = 4
y = (7/3)x + 4
or, since you are given a point and a slope, try using the point-slope form of the line:
y-11 = (7/3)(x-3)
That's good enough for me. What you want depends on what you mean by "the equation" of a line.
To find the equation of a line in slope-intercept form, we use the formula: y = mx + b, where m is the slope of the line and b is the y-intercept.
Given that the line passes through (3, 11) with a slope of 7/3, we can substitute these values into the equation.
The slope, m, is 7/3, so we have: y = (7/3)x + b.
To find the y-intercept, we substitute the coordinates of the point (3, 11) into the equation and solve for b.
11 = (7/3) * 3 + b
11 = 7 + b
b = 11 - 7
b = 4
The y-intercept, b, is 4.
Therefore, the equation of the line in slope-intercept form is: y = (7/3)x + 4.
To find the equation of a line in slope-intercept form (y = mx + b), we need to determine the slope (m) and the y-intercept (b).
Given that the line passes through the point (3,11) and has a slope of 7/3, we can substitute these values into the equation.
Step 1: Substitute the values into the slope-intercept form equation.
y = mx + b
11 = (7/3)(3) + b
Note that the slope-intercept form equation is now in the form y = mx + b, with y = 11, slope (m) = 7/3, and x = 3. We just need to solve for b.
Step 2: Simplify the equation.
11 = 7/3 * 3 + b
11 = 7 + b
11 - 7 = b
4 = b
Step 3: Substitute the values of m and b back into the slope-intercept form equation.
The equation of the line in slope-intercept form is:
y = (7/3)x + 4