Question:
The equation of the line passing through the point (-3,7) with slope zero is
The equation of the line passing through the point (-3,7) with slope zero is
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Geometry Tip: A line with "slope zero" is always horizontal and its equation is just "$y = (\text{the y-coordinate})$". A line with an "undefined slope" is vertical and its equation is "$x = (\text{the x-coordinate})$".
Updated On: Apr 30, 2026
- $x=7$
- $y=7$
- $x=-3$
- $y=-3$
- $x=0$
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The Correct Option is B
Solution and Explanation
Concept:
The equation of any straight line can be found using the point-slope form: $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope. A slope of zero indicates a perfectly horizontal line, meaning the $y$-value remains constant regardless of the $x$-value.
Step 1: Identify the given parameters.
The line passes through the point $(x_1, y_1) = (-3, 7)$. The slope of the line is given as $m = 0$.
Step 2: State the point-slope formula.
The standard point-slope equation is: $$y - y_1 = m(x - x_1)$$
Step 3: Substitute the parameters into the formula.
Plug the known values into the equation: $$y - 7 = 0(x - (-3))$$
Step 4: Simplify the right side of the equation.
Because the slope is zero, the entire right side of the equation is multiplied by zero, neutralizing the $x$ term: $$y - 7 = 0$$
Step 5: Isolate y to find the final equation.
Add 7 to both sides of the equation to put it in its simplest form: $$y = 7$$ Hence the correct answer is (B) $y=7$.
The equation of any straight line can be found using the point-slope form: $y - y_1 = m(x - x_1)$, where $(x_1, y_1)$ is a point on the line and $m$ is the slope. A slope of zero indicates a perfectly horizontal line, meaning the $y$-value remains constant regardless of the $x$-value.
Step 1: Identify the given parameters.
The line passes through the point $(x_1, y_1) = (-3, 7)$. The slope of the line is given as $m = 0$.
Step 2: State the point-slope formula.
The standard point-slope equation is: $$y - y_1 = m(x - x_1)$$
Step 3: Substitute the parameters into the formula.
Plug the known values into the equation: $$y - 7 = 0(x - (-3))$$
Step 4: Simplify the right side of the equation.
Because the slope is zero, the entire right side of the equation is multiplied by zero, neutralizing the $x$ term: $$y - 7 = 0$$
Step 5: Isolate y to find the final equation.
Add 7 to both sides of the equation to put it in its simplest form: $$y = 7$$ Hence the correct answer is (B) $y=7$.
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