Using point-slope form, write the equation of the line that describes this scenario. Then, rewrite the equation in slope-intercept form.
At a chili cook off, people pay $0.50 for each sample bowl of chili. The total cost was $4.50 for 3 bowls of chili.
1. Point-Slope Form Equation:
2. Slope-Intercept Form Equation:
1. Point-Slope Form Equation:
The point-slope form of a linear equation is y - y1 = m(x - x1), where m is the slope and (x1, y1) is a point on the line.
In this case, the slope is the cost per bowl of chili, which is $0.50, and the point (3, $4.50) represents the number of bowls and the total cost.
Therefore, the equation in point-slope form is y - 4.50 = 0.50(x - 3).
2. Slope-Intercept Form Equation:
To rewrite the equation in slope-intercept form, we need to solve for y.
First, distribute 0.50 to the expression (x - 3):
y - 4.50 = 0.50x - 1.50.
Next, add 4.50 to both sides of the equation to isolate y:
y = 0.50x - 1.50 + 4.50.
Finally, simplify the expression on the right side of the equation:
y = 0.50x + 3.00.
Therefore, the equation in slope-intercept form is y = 0.50x + 3.00.