Final answer:
The x-intercept of line r, which is parallel to the line represented by 2x-3y=-18 with a y-intercept of -2, is found to be 3.
Step-by-step explanation:
The student has asked for the x-intercept of a line (line r) that is parallel to the graph of the equation 2x - 3y = -18 and has a y-intercept of -2.
To solve this, we will first understand that since line r is parallel to the given linear equation, they will have identical slopes. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. The equation of the given line can be rearranged into slope-intercept form to find its slope.
First, isolate y: 3y = 2x +18 and then y = (2/3)x + 6. Hence, the slope m is 2/3.
Since line r has the same slope, its equation will be y = (2/3)x - 2 because the y-intercept b is given as -2.
To find the x-intercept, set y to 0 and solve for x: 0 = (2/3)x - 2. Multiplying both sides by 3 to eliminate the fraction gives 0 = 2x - 6, and adding 6 to both sides gives 6 = 2x. Finally, divide by 2 to solve for the x-intercept: x = 3.
The x-intercept of line r is 3.