Question

annie was given two pieces of information and must write the equation of a line. she knows the line crosses the y - axis at the point (0, 6) and has a slope of 7. what is the equation of the line? desmos graphing calculator (partial view of desmos graph with grid from -10 to 10 on x and y axes) \\(\boldsymbol{\circ}\\) a. \\(y = 6x + 7\\) \\(\boldsymbol{\circ}\\) b. \\(y = -6x + 7\\) \\(\boldsymbol{\circ}\\) c. \\(y = 7x - 6\\) \\(\boldsymbol{\circ}\\) d. \\(y = 7x + 6\\)

Explanation:

Step1: Recall slope - intercept form

The slope - intercept form of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept (the value of $y$ when $x = 0$).

Step2: Identify $m$ and $b$

We know that the slope $m = 7$ (given) and the line crosses the $y$ - axis at $(0,6)$. The y - intercept $b$ is the $y$ - coordinate of the point where the line crosses the $y$ - axis, so $b = 6$.

Step3: Substitute $m$ and $b$ into the formula

Substitute $m = 7$ and $b = 6$ into $y=mx + b$. We get $y=7x + 6$.

Answer:

D. $y = 7x+6$