Determine the Linear Equation: Given Slope 1.5 and Point (3, 7.5)

Video Solution

Solution Steps

00:00 Find the algebraic representation of the function

00:03 We'll use the straight line equation

00:09 We'll substitute the point according to the given data

00:15 We'll substitute the line's slope according to the given data

00:21 We'll continue solving to find the intersection point

00:35 We'll isolate intersection point B

00:41 This is the intersection point with the Y-axis

00:46 Now we'll substitute the intersection point and slope in the line equation

01:02 We'll factor out 1.5 from the parentheses

01:07 And this is the solution to the question

Step-by-Step Solution

To solve the problem of finding the equation of the line:

Step 1: Identify the given information: slope $m = 1\frac{1}{2} = \frac{3}{2}$ , and point $(x_1, y_1) = (3, 7\frac{1}{2}) = (3, \frac{15}{2})$ .
Step 2: Use the point-slope formula $y - y_1 = m(x - x_1)$ .
Step 3: Substitute the given slope and point into the formula: $y - \frac{15}{2} = \frac{3}{2}(x - 3)$ .
Step 4: Distribute the slope on the right side: $y - \frac{15}{2} = \frac{3}{2}x - \frac{9}{2}$ .
Step 5: Add $\frac{15}{2}$ to both sides to solve for $y$ : $y = \frac{3}{2}x - \frac{9}{2} + \frac{15}{2}$ .
Step 6: Simplify the right side: $y = \frac{3}{2}x + 3$ .
Step 7: Compare this expression to the provided choices to find a match. The form is the same as choice $y=1\frac{1}{2}(x+2)$ , rewritten correctly as $y = \frac{3}{2}(x + 2)$ .

Therefore, the expression that corresponds to the line is $y = 1\frac{1}{2}(x+2)$ .