Question

questions: 1. identify the slope. 2. write the equation of the line in slope - intercept form. 3. predict the value of y when x = 6. example problem 1: from a table of values

Explanation:

Step1: Calculate the slope

The slope $m$ formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(1,4)$ and $(x_2,y_2)=(2,7)$. Then $m=\frac{7 - 4}{2 - 1}=3$.

Step2: Find the y - intercept

The slope - intercept form is $y=mx + b$. Using the point $(1,4)$ and $m = 3$, we substitute into the equation: $4=3\times1 + b$. Solving for $b$, we get $b=4 - 3=1$. So the equation is $y = 3x+1$.

Step3: Predict the y - value

Substitute $x = 6$ into the equation $y=3x + 1$. Then $y=3\times6+1=19$.

Answer:

1. The slope is 3.
2. The equation of the line in slope - intercept form is $y = 3x+1$.
3. When $x = 6$, $y=19$.