Question

1 multiple choice 2 points which is an equation of the line that passes through the point (1,4) and has a slope of 3? y = 3x - 1 y = 3x + 4 y = 3x + 1 y = \frac{1}{3}x + 4 2 multiple choice 2 points the accompanying diagram shows two similar triangles. which proportion could be used to solve for x? \frac{32}{x}=\frac{12}{15} \frac{32}{12}=\frac{15}{x} \frac{24}{9}=\frac{15}{x} \frac{x}{24}=\frac{9}{15}

Explanation:

Step1: Use the point - slope form for the first question

The point - slope form of a line is \(y - y_1=m(x - x_1)\), where \((x_1,y_1)=(1,4)\) and \(m = 3\).
Substitute into the formula: \(y-4 = 3(x - 1)\).

Step2: Simplify the equation

Expand \(y-4=3x-3\).
Add 4 to both sides: \(y=3x-3 + 4\), so \(y=3x + 1\).

Step3: Use the property of similar triangles for the second question

For similar triangles, the ratios of corresponding sides are equal.
The side of length 24 in the first triangle corresponds to the side of length 9 in the second triangle, and the side of length \(x\) in the first triangle corresponds to the side of length 15 in the second triangle.
So, \(\frac{24}{9}=\frac{x}{15}\).

Answer:

1. \( y = 3x+1\)
2. \(\frac{24}{9}=\frac{x}{15}\)